A Phase 1/2 Open-Label Study Evaluating the Safety and Efficacy of ST-067 in Combination With CD19-Directed CAR T-Cell Therapy in Patients With Relapsed/Refractory (R/R) Large B-Cell Lymphoma (LBCL)

Inclusion Criteria: * Male or female \>= 18 years of age at the time of consent * Patients with LBCL (including diffuse large B-cell lymphoma \[DLBCL\] not otherwise specified \[including DLBCL arising from indolent lymphoma\], high-grade B-cell lymphoma, primary mediastinal large B-cell lymphoma, and follicular lymphoma grade 3B) with at least 2 lines of systemic therapy and an Food and Drug Administration (FDA)-approved indication for treatment with liso-cel * Fluorodeoxyglucose (FDG)-avid disease on PET imaging before lymphodepletion or pathology evidence of active disease * Evidence of CD19 expression on any prior or current tumor specimen or a high likelihood of CD19 expression based on disease histology * Karnofsky performance status \>= 60% * Adequate bone marrow function for lymphodepletion chemotherapy defined as: absolute neutrophil count (ANC) \>= 1000 cells/mm\^3, platelets \>= 50,000 cells/mm\^3, and hemoglobin \>= 8 g/dL, unless the cytopenias are due to bone marrow involvement by lymphoma in the opinion of the principal investigator (PI) * Calculated creatinine clearance (Cockcroft/Gault) \> 30 mL/min/1.73 m\^2 * Alanine aminotransferase (ALT) and aspartate aminotransferase (AST) =\< 3 x upper limit of normal (ULN) (or \< 5 x ULN for subjects with lymphomatous infiltration of the liver) and total bilirubin =\< 2 (or \< 3.0 for subjects with Gilbert's syndrome, lymphomatous infiltration of the liver, or hemolysis) * Adequate pulmonary function based on pulmonary function testing (PFT), defined as forced expiratory volume in 1 second (FEV1) and FEV1/forced vital capacity (FVC) ratio of \>= 60% of predicted value and diffusing capacity of the lung for carbon monoxide (DLCO; corrected) \>= 40% of predicted value * Adequate cardiac function, defined as left ventricular ejection fraction (LVEF) \>= 40% as assessed by echocardiogram or multiple uptake gated acquisition (MUGA) * Women of reproductive potential (defined as all women physiologically capable of becoming pregnant) must agree to use suitable methods of contraception for at least 30 days after the last dose of study therapy (ST-067) * Males who have partners of reproductive potential must agree to use an effective barrier contraceptive method for at least 90 days after the last dose of study therapy (ST-067) * Ability to understand and provide informed consent * Able and willing to comply with study visit schedule and procedures, including tumor biopsy where feasible and with acceptable risk Exclusion Criteria: * Planned use of out-of-specification liso-cel product * History of another malignancy. The following are exceptions to this criterion: * Adequately treated basal cell or squamous cell carcinoma of the skin. * In situ prostate, ductal breast carcinoma breast, and cervical carcinoma. * Adequately treated papillary, noninvasive bladder cancer. * Other adequately treated stage 1 or 2 cancers currently in complete remission. * Any other cancer that has been in remission for \>= 2 years * Planned use of therapeutic doses of corticosteroids (\> 20 mg/day prednisone or equivalent) or other systemic immunosuppression within 7 days prior to leukapheresis or within 72 hours prior to liso-cel infusion. Topical and/or inhaled steroids are permitted * Prior treatment with any CD19 CAR T-cell therapy * For allogeneic hematopoietic cell transplant recipients, active graft versus host disease (GVHD) and/or systemic GVHD therapy within 30 days prior to planned leukapheresis * Known active hepatitis B (detectable hepatitis B deoxyribonucleic acid \[DNA\]) or hepatitis C (detectable hepatitis C ribonucleic acid \[RNA\]) * Known human immunodeficiency virus (HIV) infection * Pregnant or breastfeeding women * Prior treatment with any IL-1 or IL-18 agonist and/or biosimilar agents, or an investigational agent within 4 weeks or 5 half-lives, whichever is shorter, prior to start of lymphodepletion * Active autoimmune or inflammatory disorders (including inflammatory bowel disease \[e.g., ulcerative colitis, Crohn's disease\], celiac disease, or other serious chronic gastrointestinal conditions associated with diarrhea, autoimmune vasculitis, systemic lupus erythematosus, Wegener syndrome \[granulomatosis with polyangiitis\], myasthenia gravis, Graves' disease, rheumatoid arthritis, hypophysitis, uveitis, etc.) requiring immunosuppressive therapy. The following are exceptions to this criterion: * Vitiligo. * Alopecia. * Hypothyroidism (e.g., following Hashimoto syndrome) stable on hormone replacement. * Type 1 diabetes mellitus. * Psoriasis not requiring systemic treatment. * Conditions considered to be low risk of serious deterioration by the PI * History of any one of the following cardiovascular conditions within the past 6 months, unless clearance by a cardiologist is obtained: class III or IV heart failure as defined by the New York Heart Association (NYHA), cardiac angioplasty or stenting, myocardial infarction, or unstable angina. History of other clinically significant cardiac disease that, in the opinion of the PI or designee, is a contraindication to study treatment is also excluded * Significant electrocardiogram (ECG) abnormalities, including unstable cardiac arrhythmia requiring medication, second-degree atrioventricular (AV) block type II, third-degree AV block, \>= grade 2 bradycardia, or QT interval corrected using Fridericia's formula \> 500 ms irrespective of gender * History or presence of clinically relevant central nervous system (CNS) pathology, such as epilepsy, seizure, paresis, aphasia, stroke, severe brain injuries, dementia, Parkinson's disease, cerebellar disease, or psychosis that in the opinion of the PI is a contraindication to study treatment. * Patients with active parenchymal CNS involvement by malignancy will be excluded. Patients with prior or current secondary leptomeningeal CNS disease are eligible. CNS disease prophylaxis must be stopped at least 1 week prior to liso-cel infusion * History of solid organ transplantation * Active, serious, and uncontrolled infection(s)